The intraglobular electrostatic field of an enzyme. II. Effect of environment polarization

The influence of polarization of surrounding medium on the intraglobular electric field of the alpha-chymotrypsin molecule is considered. The polarization is taken into account by the image charges method, the proper approximations for calculation of the fields due to intraglobular and surface charges are suggested. The polarization of surroundings does not change the qualitative picture of the electric field in the active center of the alpha-chymotrypsin molecule set up by protein dipoles, but reduces almost to zero the intraglobular field set up by surface ions.     

Electric field detection in sawfish and shovelnose rays

In the aquatic environment, living organisms emit weak dipole electric fields, which spread in the surrounding water. Elasmobranchs detect these dipole electric fields with their highly sensitive electroreceptors, the ampullae of Lorenzini. Freshwater sawfish, Pristis microdon, and two species of shovelnose rays, Glaucostegus typus and Aptychotrema rostrata were tested for their reactions towards weak artificial electric dipole fields. The comparison of sawfishes and shovelnose rays sheds light on the evolution and function of the elongated rostrum ('saw') of sawfish, as both groups evolved from a shovelnose ray-like ancestor. Electric stimuli were presented both on the substrate (to mimic benthic prey) and suspended in the water column (to mimic free-swimming prey). Analysis of around 480 behavioural sequences shows that all three species are highly sensitive towards weak electric dipole fields, and initiate behavioural responses at median field strengths between 5.15 and 79.6 nVcm(-1). The response behaviours used by sawfish and shovelnose rays depended on the location of the dipoles. The elongation of the sawfish's rostrum clearly expanded their electroreceptive search area into the water column and enables them to target free-swimming prey.     

Electrostatic field effects on membrane domain segregation and on lateral diffusion

Natural membranes are organized structures of neutral and charged molecules bearing dipole moments which generate local non-homogeneous electric fields. When subjected to such fields, the molecules experience net forces that can modify the lipid and protein organization, thus modulating cell activities and influencing (or even dominating) the biological functions. The energetics of electrostatic interactions in membranes is a long-range effect which can vary over distance within r⁻¹ to r⁻³. In the case of a dipole interacting with a plane of dipoles, e.g. a protein interacting with a lipid domain, the interaction is stronger than two punctual dipoles and depends on the size of the domain. In this article, we review several contributions on how electrostatic interactions in the membrane plane can modulate the phase behavior, surface topography and mechanical properties in monolayers and bilayers.     

Reproduction of correct electrostatic field by charges and dipoles on a closed surface

A general algorithm based on the Green function theorem has been developed to correctly reproduce electrostatic fields inside a closed space by point charges and point dipoles on the surface surrounding the space. For actual computations, limited numbers of point charges, including charge pairs replacing point dipoles, are enough to approximate the inner fields. As examples, reaction fields were reproduced by the current surface charges and dipoles for the dielectric models, where a monopole, dipole, or quadrupole was individually set at the center in a vacuum sphere surrounded by high dielectric continuum. The potentials due to those reaction fields agree well with the analytical ones. As an application of this method to the analysis of the electronic structure of the active site of a protein, a combination of the continuum dielectric model and ab initio molecular orbital calculation was carried out. Other applications to molecular dynamics and quantum mechanical calculations are also discussed.     

Pseudo-spin model for the microtubule wall in external field

Microtubules (MTs) in the cytoskeletons of eukaryotic cells provide a wide range of microskeletal and micromuscular functionalities. Some evidence has indicated that they can serve as a medium for intracellular signaling processing. In this paper, for the inherent symmetry structures and the electric properties of tubulin dimers, the microtubule (MT) is treated as a one-dimensional ferroelectric system. The nonlinear dynamics of the dimer electric dipoles is described by virtue of the double-well potential and the physical problem is further mapped onto the pseudo-spin system. In addition, the effect of the external electric field on the MT has been taken into account.     

Effects of aligned α‐helix peptide dipoles on experimental electrostatic potentials

Aligned protein α‐helix dipoles have been implicated in protein function and structure. The recent breakthroughs in high‐resolution electron microscopy (EM) of macromolecules makes it possible to explore fundamental aspects of structural biology at the detailed molecular level. The electrostatic potential (ESP) generated by aligned protein α‐helix dipole should be observable in high‐resolution EM maps despite the fact that the effect may be partially screened by induced electric fields. Here, we show that aligned backbone dipoles in protein α‐helices account for long‐range features in the protein ESP functions. Our results are consistent with experimental EM maps and density functional theory calculations, including direct Fourier summation for proper calculation of the ESP due to the nonlocal nature of the ESP function from aligned dipoles and other partial atomic charges.     

Interaction of phospholipids with Ca2+ ions. On the role of the phospholipid head groups

Neutral phospholipids play an important role in Ca2+ binding to biomembranes, in particular if the membrane carries a net negative surface charge due to charged lipids or proteins. The concentration of Ca2+ ions in the plane of the phospholipid head groups can be enhanced by at least two orders of magnitude compared to bulk solution. Ca2+ binding furthermore changes the orientation of the phospholipid head groups which is accompanied by variations of the local membrane dipole potential of the order of 10(5) V/cm. Such high electric fields could entail conformational changes of membrane-bound proteins and the Ca2(+)-induced reorientation of the lipid dipoles could thus play a regulatory role in membrane function.     

High-frequency electric field and radiation characteristics of cellular microtubule network

Microtubules are important structures in the cytoskeleton, which organizes the cell. Since microtubules are electrically polar, certain microtubule normal vibration modes efficiently generate oscillating electric field. This oscillating field may be important for the intracellular organization and intercellular interaction. There are experiments which indicate electrodynamic activity of variety of cells in the frequency region from kHz to GHz, expecting the microtubules to be the source of this activity. In this paper, results from the calculation of intensity of electric field and of radiated electromagnetic power from the whole cellular microtubule network are presented. The subunits of microtubule (tubulin heterodimers) are approximated by elementary electric dipoles. Mechanical oscillation of microtubule is represented by the spatial function which modulates the dipole moment of subunits. The field around oscillating microtubules is calculated as a vector superposition of contributions from all modulated elementary electric dipoles which comprise the cellular microtubule network. The electromagnetic radiation and field characteristics of the whole cellular microtubule network have not been theoretically analyzed before. For the perspective experimental studies, the results indicate that macroscopic detection system (antenna) is not suitable for measurement of cellular electrodynamic activity in the radiofrequency region since the radiation rate from single cells is very low (lower than 10?2? W). Low noise nanoscopic detection methods with high spatial resolution which enable measurement in the cell vicinity are desirable in order to measure cellular electrodynamic activity reliably.     

The influence of conductivity changes in boundary element compartments on the forward and inverse problem in electroencephalography and magnetoencephalography.

Source localization based on magnetoencephalographic and electroencephalographic data requires knowledge of the conductivity values of the head. The aim of this paper is to examine the influence of compartment conductivity changes on the neuromagnetic field and the electric scalp potential for the widely used three compartment boundary element models. Both the analysis of measurement data and the simulations with dipoles distributed in the brain produced two significant results. First, we found the electric potentials to be approximately one order of magnitude more sensitive to conductivity changes than the magnetic fields. This was valid for the field and potential topology (and hence dipole localization), and for the amplitude (and hence dipole strength). Second, changes in brain compartment conductivity yield the lowest change in the electric potentials topology (and hence dipole localization), but a very strong change in the amplitude (and hence in the dipole strength). We conclude that for the magnetic fields the influence of compartment conductivity changes is not important in terms of dipole localization and strength estimation. For the electric potentials however, both dipole localization and strength estimation are significantly influenced by the compartment conductivity.     

Electric field generated by axial longitudinal vibration modes of microtubule

Microtubules are electrically polar structures fulfilling prerequisites for generation of oscillatory electric field in the kHz to GHz region. Energy supply for excitation of elasto-electrical vibrations in microtubules may be provided from GTP-hydrolysis; motor protein–microtubule interactions; and energy efflux from mitochondria. We calculated electric field generated by axial longitudinal vibration modes of microtubules for random, and coherent excitation. In case of coherent excitation of vibrations, the electric field intensity is highest at the end of microtubule. The dielectrophoretic force exerted by electric field on the surrounding molecules will influence the kinetics of microtubule polymerization via change in the probability of the transport of charge and mass particles. The electric field generated by vibrations of electrically polar cellular structures is expected to play an important role in biological self-organization.     

Measurement and computation of the dipole moment of globular proteins III: Chymotrypsin

The dipole moments of alpha- and gamma-chymotrypsin are determined experimentally using the dielectric constant measuring method. The values thus obtained are compared with the results of the electric dichroism measurements for alpha-chymotrypsins by other investigators. The agreement is reasonably good, if not satisfactory. The cause of difference appears to be due to the difficulty of finding the correct internal field. The interaction between two neighboring dipoles is found to be a minor component of the local fields. Secondly, the dipole moment of alpha-chymotrypsin was computed using Protein Data Bases. The dipole moment of proteins consists of two major components, the moment due to fixed surface charges and the core moment due to polar chemical bonds. The method of calculation was described in detail in previous papers. The pK shifts of polar side chains were calculated using the methods of Tanford et al. and its modification by Warshel et al. The agreement between measured and calculated dipole moments is satisfactory.     

Gene transfer into mouse lyoma cells by electroporation in high electric fields.

Electric impulses (8 kV/cm, 5 microseconds) were found to increase greatly the uptake of DNA into cells. When linear or circular plasmid DNA containing the herpes simplex thymidine kinase (TK) gene is added to a suspension of mouse L cells deficient in the TK gene and the cells are then exposed to electric fields, stable transformants are formed that survive in the HAT selection medium. At 20 degrees C after the application of three successive electric impulses followed by 10 min to allow DNA entry there result 95 (+/- 3) transformants per 10(6) cells and per 1.2 micrograms DNA. Compared with biochemical techniques, the electric field method of gene transfer is very simple, easily applicable, and very efficient. Because the mechanism of DNA transport through cell membranes is not known, a simple physical model for the enhanced DNA penetration into cells in high electric fields is proposed. According to this ' electroporation model' the interaction of the external electric field with the lipid dipoles of a pore configuration induces and stabilizes the permeation sites and thus enhances cross membrane transport.     

The different screening of electric charges and dipoles near a dielectric interface

The electric fields within a planar slab of material due to both charges and dipoles within the slab and near to its surface are simply calculated using the method of images. If the slab is immersed in a fluid of high dielectric constant the electric field within the slab due to the charge is always reduced but that of a suitably oriented electric dipole is enhanced by as much as a factor of two.     

Studies of electrons trapped in X-irradiated rhamnose crystals

The electrons trapped in single crystals of rhamnose X-irradiated at low temperature were studied by ENDOR spectroscopy. Hyperfine couplings of protons in the environs of the electron have been determined from ENDOR measurements, including those of some of the more remote carbon-bound hydrogen atoms. The likely site of electron trapping in the crystal structure of rhamnose was inferred from calculations of the electric potential generated by the dipoles of hydroxy groups about preexisting void spaces. Electron-proton distances for nonexchangeable hydrogen atoms from points within the void were calculated from the crystal structure and compared with distances obtained from hyperfine couplings. Good agreement was obtained between experimental and calculated values.     

Use of a potential of mean force to analyze free energy contributions in protein folding.

A method for calculation of the free energy of residues as a function of residue burial is proposed. The method is based on the potential of mean force, with a reaction coordinate expressed by residue burial. Residue burials are calculated from high-resolution protein structures. The largest individual contributions to the free energy of a residue are found to be due to the hydrophobic interactions of the nonpolar atoms, interactions of the main chain polar atoms, and interactions of the charged groups of residues Arg and Lys. The contribution to the free energy of folding due to the uncharged side chain polar atoms is small. The contribution to the free energy of folding due to the main chain polar atoms is favorable for partially buried residues and less favorable or unfavorable for fully buried residues. Comparison of the accessible surface areas of proteins and model spheres shows that proteins deviate considerably from a spherical shape and that the deviations increase with the size of a protein. The implications of these results for protein folding are also discussed.     

Electrical fields in membrane proteins]

The electric fields created by dipoles of the peptide bonds of alpha-helices of membrane proteins are considered. It has been shown that the electric field of the alpha-helix compensates for the loss of the Born hydration energy and promotes dissociation of the carboxyl groups located at the depth of up to 5 A from the water surface. The presence of the carboxylate anion facilitates penetration of the hydronium ion into the membrane and lowers the potential barrier by 0.1-0.2 eV (depending on the membrane thickness). A three-layer model of the reaction centre of photosynthetic bacteria is proposed. An estimate of the dielectric constant of different parts of the reaction centre is obtained by means of comparison of photoinduced electrogenetic transmembrane potential displacement with structural data. Estimates of the electric potentials at the electron transfer chain cofactors induced by the alpha-helical segments of the reaction centre protein are given. It is shown that the asymmetry in the location of alpha-helices affects significantly the redox potentials of the electron carriers and lead to a kinetic advantage of the A-chain of electron transfer over the B-chain.     

Brownian dynamics study of ion transport in the vestibule of membrane channels.

Brownian dynamics simulations have been carried out to study the transport of ions in a vestibular geometry, which offers a more realistic shape for membrane channels than cylindrical tubes. Specifically, we consider a torus-shaped channel, for which the analytical solution of Poisson's equation is possible. The system is composed of the toroidal channel, with length and radius of the constricted region of 80 A and 4 A, respectively, and two reservoirs containing 50 sodium ions and 50 chloride ions. The positions of each of these ions executing Brownian motion under the influence of a stochastic force and a systematic electric force are determined at discrete time steps of 50 fs for up to 2.5 ns. All of the systematic forces acting on an ion due to the other ions, an external electric field, fixed charges in the channel protein, and the image charges induced at the water-protein boundary are explicitly included in the calculations. We find that the repulsive dielectric force arising from the induced surface charges plays a dominant role in channel dynamics. It expels an ion from the vestibule when it is deliberately put in it. Even in the presence of an applied electric potential of 100 mV, an ion cannot overcome this repulsive force and permeate the channel. Only when dipoles of a favorable orientation are placed along the sides of the transmembrane segment can an ion traverse the channel under the influence of a membrane potential. When the strength of the dipoles is further increased, an ion becomes detained in a potential well, and the driving force provided by the applied field is not sufficient to drive the ion out of the well. The trajectory of an ion navigating across the channel mostly remains close to the central axis of the pore lumen. Finally, we discuss the implications of these findings for the transport of ions across the membrane.